Large-time behaviour of SEEs with Volterra noise
A talk in the Bielefeld Stochastic Afternoon series by
Petr Čoupek from Prague
| Abstract: | The talk will be devoted to large-time behaviour of solutions to linear stochastic evolution equations driven by additive two-sided regular Volterra-type processes. These processes need not be Gaussian, Markov, or (semi)martingales but admit a certain covariance structure instead.The main examples include the fractional Brownian motion of $H>1/2$ and the Rosenblatt process. The solution is understood in the mild sense and takes values in a separable Hilbert space. Sufficient conditions for the existence of a limiting measure and strict stationarity of the solution process will be presented and an example for which these conditions are also necessary will be given. This example also shows that the regular fractional Brownian motion of $H>1/2$ may be worse than the Wiener process in terms of stabilising equations. Additionally, the results will be applied to the stochastic heat equation driven by noise which is Rosenblatt in time and can be white or correlated in space. |